This passage is about the speech of President Jackson in Congress, where he defended the process of remorse of the Indians.
The use of the word "progessive" refers to the continuation of a process begun earlier, where the Indians were massacred and expelled from their territories to the detriment of the white man's civilization. The former president used that term as a way to slow down an attitude that today would be understood as barbarism, but one that is part of US history.
The Cyrillic alphabet was a combonation of Greek, Egyptian, and Hebrew.
Yes, technically it is true that Mosques are centers of Islamic worship, although it should be noted that Muslim people (who usually worship in the Islamic faith) can pray in a variety of places.